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Modelling smooth- and transitionally rough-wall turbulent channel flow by leveraging inner–outer interactions and principal component analysis

Published online by Cambridge University Press:  29 January 2019

Sicong Wu Open the ORCID record for Sicong Wu [Opens in a new window] ,
Kenneth T. Christensen Open the ORCID record for Kenneth T. Christensen [Opens in a new window]  and
Carlos Pantano Open the ORCID record for Carlos Pantano [Opens in a new window]
Sicong Wu*
Affiliation:
Department of Mechanical Science and Engineering, University of Illinois at Urbana-Champaign, Urbana, IL 61801, USA
Kenneth T. Christensen
Affiliation:
Department of Aerospace and Mechanical Engineering and Civil and Environmental Engineering and Earth Sciences, University of Notre Dame, Notre Dame, IN 46556, USA International Institute for Carbon Neutral Energy Research (WPI-I2CNER), Kyushu University, Fukuoka 819-0385, Japan
Carlos Pantano
Affiliation:
Department of Mechanical Science and Engineering, University of Illinois at Urbana-Champaign, Urbana, IL 61801, USA
*
†Email address for correspondence: swu52@illinois.edu
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Abstract

Direct numerical simulations (DNS) of turbulent channel flow over rough surfaces, formed from hexagonally packed arrays of hemispheres on both walls, were performed at friction Reynolds numbers $Re_{\unicode[STIX]{x1D70F}}=200$, $400$ and $600$. The inner normalized roughness height $k^{+}=20$ was maintained for all Reynolds numbers, meaning all flows were classified as transitionally rough. The spacing between hemispheres was varied within $d/k=2$–$4$. The statistical properties of the rough-wall flows were contrasted against a complementary smooth-wall DNS at $Re_{\unicode[STIX]{x1D70F}}=400$ and literature data at $Re_{\unicode[STIX]{x1D70F}}=2003$ revealing strong modifications of the near-wall turbulence, although the outer-layer structure was found to be qualitatively consistent with smooth-wall flow. Amplitude modulation (AM) analysis was used to explore the degree of interaction between the flow in the roughness sublayer and that of the outer layer utilizing all velocity components. This analysis revealed stronger modulation effects, compared to smooth-wall flow, on the near-wall small-scale fluctuations by the larger-scale structures residing in the outer layer irrespective of roughness arrangement and Reynolds number. A predictive inner–outer model based on these interactions, and exploiting principal component analysis (PCA), was developed to predict the statistics of higher-order moments of all velocity fluctuations, thus addressing modelling of anisotropic effects introduced by roughness. The results show excellent agreement between the predicted near-wall statistics up to fourth-order moments compared to the original statistics from the DNS, which highlights the utility of the PCA-enhanced AM model in generating physics-based predictions in both smooth- and rough-wall turbulence.

JFM classification

Turbulent Flows: Turbulence modelling Turbulent Flows: Turbulence simulation Turbulent Flows: Turbulent boundary layers
Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 863 , 25 March 2019 , pp. 407 - 453
Copyright
© 2019 Cambridge University Press 

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